Learn Like a GEM Unit 6 Collecting Data GL Practice Study Guide

Learning Objectives and Outcomes

The "Learn Like a GEM" program for Unit-6 (dated 5-26) focuses on "Collecting Data" through GL Assessment practice. This training is designed to enable students to:

• Practice for GL Assessments to improve reasoning and problem-solving abilities.

• Enhance literacy and numeracy skills.

• Develop exam confidence and accuracy.

• Build overall exam readiness through the Knowledge Component of the curriculum.

Number Representation and Place Value

Comprehensive understanding of numerical notation and the value of digits within large numbers is verified through the following examples:

• Figures to Words Conversion: The number "five thousand, one hundred and nine" is written in figures as $5109$.

• Place Value Identification: In the number $7240$, the value of the digit $7$ is identified as $7\text{ thousands}$.

• Number Line Estimation: On a number line scaled between $1200$ and $1400$, a specific point (Point C) represents the value $1250$.

• Roman Numerals and Multi-Step Arithmetic: Calculating the product of Roman numerals requires conversion to Arabic numerals:

  • $XXVI = 26$

  • $XLI = 41$

  • Calculation: $26 \times 41 = 1066$

  • The resulting Roman numeral is $MLXVI$.

Arithmetic, Sequences, and Algebraic Logic

• Number Sequences: Logic patterns involve identifying constant differences. In the sequence $393, 384, 375, \dots, 357$, the pattern is an arithmetic progression with a common difference of $-9$. The missing number is $375 - 9 = 366$. (Note: Assessment option D provided was $369$, but the mathematical logic follows the $-9$ rule).

• Properties of One and Zero: Operation identity is tested with equations like $123 \div \square = 123$, where the missing value is the identity element $1$.

• Basic Algebra: Solving for unknown variables, such as in the equation $a - 9 = 10$. Solving for $a$ leads to $a = 10 + 9 = 19$.

• Reverse Operations (Inverse Thinking): In a "think of a number" problem:

  1. Take a number $x$.

  2. Multiply by $2$ ($2x$).

  3. Subtract $4$ ($2x - 4 = 10$).

  4. Solve: $2x = 14 \rightarrow x = 7$.

• Multiplying by Powers of Ten: Simple decimal shift operations, such as $3.6 \times 10 = 36$.

• Multiplication and Division: Determining quotients like $105 \div \square = 21$ entails finding the factor $5$. Complex multiplication, such as finding the total travel of a ship going $528 \text{ nautical miles/day}$ for $15\text{ days}$, results in $7920 \text{ nautical miles}$.

• Indices and Square Numbers:

  • The square of a number, denoted as $3^2$, is calculated as $3 \times 3 = 9$.

  • Recognition of square numbers is essential; for example, the numbers $9$, $36$, and $81$ are alike because they are all square numbers ($3^2$, $6^2$, and $9^2$).

• Logical Comparative Instructions: Given a starting number of $5$, different instructions aim for a target of $17$:

  • Halve ($2.5$), add six ($8.5$), double ($17$).

  • Multiply by four ($20$), subtract three ($17$).

  • Triple ($15$), add two ($17$).

  • Add three ($8$), double ($16$) — This instruction fails to reach 17.

  • Multiply by ten ($50$), subtract sixteen ($34$), halve ($17$).

• Algebraic Manipulations with Large Components: Solving for missing values in equations like $27 \times 99 = 2700 - \square$. Since $27 \times 99 = 27 \times (100 - 1) = 2700 - 27$, the missing value is $27$.

Fractions, Decimals, and Percentages

• Shaded Areas: Fractions of a whole are determined by counting shaded segments versus total segments (e.g., $3/8$ of a shape being shaded).

• Percentage Calculations: To find what percentage $50p$ is of $\pounds 5$, the conversion is $\frac{50}{500} = \frac{1}{10} = 10\%$.

• Fraction of a Quantity: Taking $\frac{2}{3}$ of a set of $36 \text{ sweets}$ is calculated as $(36 \div 3) \times 2 = 24 \text{ sweets}$.

• Ordering Fractions: Arranging fractions by finding common denominators. Sorting from largest to smallest: $\frac{7}{8}, \frac{3}{4} (\frac{6}{8}), \frac{5}{8}, \frac{1}{2} (\frac{4}{8}), \frac{1}{4} (\frac{2}{8})$.

• Percentage of Quantity: Finding $60\%$ of $50$ is calculated as $0.60 \times 50 = 30$.

• Composite Fraction Problems: Sharing a pizza with $6$ equal pieces:

  • Ali eats $\frac{1}{3}$ of the total: $\frac{1}{3} \times 6 = 2 \text{ pieces}$.

  • Remainder is $4 \text{ pieces}$.

  • Sister eats $\frac{1}{2}$ of the remaining pieces: $\frac{1}{2} \times 4 = 2 \text{ pieces}$.

  • Pieces left: $6 - 2 - 2 = 2 \text{ pieces}$, which represents $\frac{2}{6}$ or $\frac{1}{3}$ of the pizza.

Measurement, Time, and Rates

• Length Addition: An individual at $1.43 \text{ metres}$ who grows another $2 \text{ centimetres}$ ($0.02 \text{ m}$) becomes $1.45 \text{ m}$ tall.

• Volume and Estimation:

  • Subtraction of liquid volumes: A juggling of units where a $1 \text{ litre } (1000 \text{ ml})$ jug fills a $700 \text{ ml}$ jar, leaving $300 \text{ ml}$ or $0.3 \text{ litres}$ in the jug.

  • General estimation for daily objects: A standard mug holds approximately $300 \text{ millilitres}$.

• Weight Conversion: Calculating the total mass of $5 \text{ boxes}$ weighing $800 \text{ grams}$ each: $5 \times 800 \text{ g} = 4000 \text{ g}$, which equals $4 \text{ kg}$.

• Chronological Calculations:

  • 12-hour vs 24-hour time: "Quarter past seven in the evening" corresponds to $19:15$.

  • Journey duration: A train departing at $10.20$ and arriving at $11.15$ has a travel time of $55 \text{ minutes}$.

  • Timetable analysis: A train leaving East Croydon at $23:27$ and arriving at Victoria at $23:43$ takes $16 \text{ minutes}$.

• Cost Analysis and Savings:

  • Wendy saving $\pounds 2.50$ per week for a target of $\pounds 20$: $\pounds 20 \div \pounds 2.50 = 8 \text{ weeks}$.

  • Newspaper delivery rates: Paying $\pounds 1.40$ per $100 \text{ papers}$. For $250 \text{ papers}$, the calculation is $(2.5 \times 100) \times \pounds 1.40 = 2.5 \times 1.40 = \pounds 3.50$.

  • Discount economics: A swimming pool charges $\pounds 3.60$ for entry. A card costs $\pounds 5$ and saves $\frac{1}{6}$ of entry ($\pounds 0.60$ saved per visit). To recoup the $\pounds 5$ cost, Ken visits until savings exceed the card price relative to individual visits; effectively $5 \div 0.60 = 8.33$, though logic in problem context may vary based on net spending comparisons.

• Temperature: Mateo\'s base temperature of $37.5^{\circ}C$ rising by $3^{\circ}C$ results in a fever of $40.5^{\circ}C$.

• Cooking Procedures (Time and Mass Ratios):

  • Rule: Cook for $30 \text{ mins}$ at high temp, then $30 \text{ mins}$ per $450 \text{ g}$.

  • If total time is $2 \text{ hours } (120 \text{ mins})$:

  • Initial time: $30 \text{ mins}$.

  • Remaining time: $120 - 30 = 90 \text{ mins}$.

  • Weight calculation: $\frac{90}{30} \times 450 \text{ g} = 3 \times 450 \text{ g} = 1350 \text{ g}$ or $1.35 \text{ kg}$.

Geometry and Spatial Reasoning

• Coordinates: Reading locations on a grid (e.g., Hills at $(3, 4)$, identifying the lighthouse at $(1, 6)$).

• Shape Filling: Determining how many small triangles are required to fill a regular hexagon ($6 \text{ triangles}$).

• Area and Tiling: Calculating how many $1 \text{ cm}^2$ squares fit into a rectangle of dimensions $6 \text{ cm} \times 3 \text{ cm}$ (Total area $18 \text{ cm}^2 = 18 \text{ squares}$).

• Identification of Polygons:

  • Quadrilaterals are four-sided shapes; identifying non-quadrilaterals among a set.

  • Identifying 3D shapes: Distinguishing a cuboid from other polyhedra.

• Angle Classification: Observations of geometric angles:

  • Acute angles: < 90^{\circ}

  • Right angles: $= 90^{\circ}$

  • Obtuse angles: Between $90^{\circ}$ and $180^{\circ}$

  • Reflex angles: > 180^{\circ}

• Ratios in Geometry: In a class of $27 \text{ children}$ with a boy-to-girl ratio of $2:1$. The class is divided into $3 \text{ parts}$ ($27 \div 3 = 9$). Boys comprise $2 \text{ parts}$ ($18 \text{ boys}$); girls comprise $1 \text{ part}$ ($9 \text{ girls}$).

• Geometric Progressions: A frog jumping towards the edge of a pond ($12 \text{ m}$ across, so $6 \text{ m}$ from center to edge). Each jump halves the distance to the edge:

  • Start: $6 \text{ m}$ from edge.

  • Jump 1: $3 \text{ m}$ remain.

  • Jump 2: $1.5 \text{ m}$ remain.

  • Jump 3: $0.75 \text{ m}$ ($75 \text{ cm}$) remain.

Data Interpretation

• Pictograms and Tables: Identifying differences in quantity (e.g., comparing number of ships in Dock A vs. Dock C where one symbol equals $12 \text{ ships}$).

• Bar Charts:

  • Calculating total hours from categories (e.g., total "out of door" hours by summing football, fishing, and cycling).

  • Proportional analysis: Given a total class size of $28$, determining which transportation category represents exactly $4 \text{ children}$ by analyzing the height of bars.

• Line Graphs:

  • Tracking growth: Analyzing a baby's weight over $8 \text{ weeks}$ to identify which specific week showed the greatest weight gain.

  • Historical data: Population graphs for Britain from $1700$. Identifying the year when the population became double that of the year $1800$.

• Weather Data: Analyzing a 12-hour chart to identify the total duration of dry conditions (e.g., $10 \text{ hours}$).

• Set Theory (Venn Diagrams): Sorting numbers into overlapping categories such as "Multiples of 4" and "Multiples of 3". A number that fits the intersection (the shaded section) must be a multiple of both ($12$, the Lowest Common Multiple).

Tables and Pricing Models

Heritage Membership Offer Pricing:

Scenario Application: Mrs. Ward joining with three children (aged 10, 12, and 15) utilizes the "Family One Adult" category, resulting in a total payment of $\pounds 46.50$.